Find the equation of the parabola with vertex at (0, 0) and focus at (0, 2).
Find the locus of the middle point of the portion of the line xcosα+ysinα=p which is intercepted between the axes, given that p remains constant.
If the point (x,−1),(3,y),(−2,3),and(−3,−2) taken in order are the vertices of a parallelogram, then find the values of xandy˙
Find the equation of the circle passing through the points (2,3)and (−1,1)and whose centre is on the line x−3y−11=0.
If A(2,−1)andB(6,5) are two points, then find the ratio in which the food of the perpendicular from (4,1) to AB divides it.
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.36x2+4y2=144